(English Medium) ICSE Class 9 - CISCE Question Bank Solutions for Mathematics

If log₁₀ 8 = 0.90; find the value of : log√32

Prove that :  (log a)² - (log b)² = log `(( a )/( b ))` . Log (ab)

If log 27 = 1.431, find the value of : log 9

If log 27 = 1.431, find the value of : log 300

Prove that :  If a log b + b log a - 1 = 0, then b^a. a^b = 10

If log₁₀ a = b, find 10^{3b - 2} in terms of a.

 If log (a + 1) = log (4a - 3) - log 3; find a.

If log₅ x = y, find 5^{2y+ 3} in terms of x.

If 2 log y - log x - 3 = 0, express x in terms of y.

Given: log₃ m = x and log₃ n = y.
Express 3^{2x - 3} in terms of m.

Given: log₃ m = x and log₃ n = y.

Write down `3^(1 - 2y + 3x)` in terms of m and n.

Given: log₃ m = x and log₃ n = y.
If 2 log₃ A = 5x - 3y; find A in terms of m and n.

Prove that:

log₁₀ 125 = 3(1 - log₁₀2).

Simplify : log (a)³ - log a

Simplify : log (a)³ ÷  log a

Given `log_x 25 - log_x 5 = 2 - log_x (1/125)` ; find x.

Given log x = 2m - n , log y = n - 2m and log z = 3m - 2n , find in terms of m and n, the value of log `(x^2y^3 ) /(z^4) `.

The diagonals of a rectangle intersect each other at right angles. Prove that the rectangle is a square.

Prove that the bisectors of interior angles of a parallelogram form a rectangle.

Draw frequency polygons for each of the following frequency distribution: 

(a) using histogram

(b) without using histogram